A study on the effects of optical gain nonuniformly distributed in one-dimensional random systems is presented. It is demonstrated numerically that even without gain saturation and mode competition, the spatial nonuniformity of gain can cause dramatic and complicated changes to lasing modes. Lasing modes are decomposed in terms of the quasimodes of the passive system to monitor the changes. As the gain distribution changes gradually from uniform to nonuniform, the amount of mode mixing increases. Furthermore, we investigate new lasing modes created by nonuniform gain distributions. We find that new lasing modes may disappear together with existing lasing modes, thereby causing fluctuations in the local density of lasing states.

A unitary transformation method is used to investigate the dynamic evolution of two multilevel atoms, in the basis of symmetric and antisymmetric states, with one atom being initially prepared in the first excited state and the other in the ground state. The unitary transformation guarantees that our calculations are based on the ground state of the atom-field system and the self-energy is subtracted at the beginning. The total Lamb shifts of the symmetric and antisymmetric states are divided into transformed shift and dynamic shift. The transformed shift is due to emitting and reabsorbing of virtual photons, by a single atom (nondynamic single atomic shift) and between the two atoms (quasi-static shift). The dynamic shift is due to the emitting and reabsorbing of real photons, by a single atom (dynamic single atomic shift) and between the two atoms (dynamic interatomic shift). The emitting and reabsorbing of virtual and real photons between the two atoms result in the interatomic shift, which does not exist for the one-atom case. The spectra at the long-time limit are calculated. If the distance between the two atoms is shorter than or comparable to the wavelength, the strong coupling between the two atoms splits the spectrum into two peaks, one from the symmetric state and the other from the antisymmetric state. The origin of the red or blue shifts for the symmetric and antisymmetric states mainly lies in the negative or positive interaction energy between the two atoms. In the investigation of the short time evolution, we find the modification of the effective density of states by the interaction between two atoms can modulate the quantum Zeno and quantum anti-Zeno effects in the decays of the symmetric and antisymmetric states.

We present exact analytical solutions describing spatial bright, trigonometric, and kink-type of self-similar waves, as well as the trains of such waves to the nonlinear Schrödinger equation appropriately modified to model beam propagation in graded-index, nonlinear fiber amplifier with an external source. We show that this model is appropriate for the self-similar propagation in asymmetric twin-core fiber amplifier. The asymmetric twin-core fiber is composed of two adjoining, closely spaced, single mode fibers in which the active one is a graded-index nonlinear fiber and the passive one is a step-index fiber. We obtain these self-similar waves using a Möbius transformation. Our procedure is applicable both for self-focusing and self-defocusing Kerr nonlinearities.

The Fourier transform-limited electromagnetic pulse has been regarded to be free of chirps for a long time. This is no longer true if the pulse duration goes down to or less than one optical cycle. We report the experimental observation of intrinsic chirps in such pulses with the sub-single-cycle terahertz (THz) waveforms obtained with a standard THz time-domain spectroscopy system. The results confirm the break down of the carrier-envelope (CE) expression for single-cycle optical pulses, and may influence the experimental measurements and theoretical modeling with single-cycle pulses.

We propose the implementation of a light source that can deterministically generate a rich variety of multimode quantum states. The desired states are encoded in the collective population of different ground hyperfine states of an atomic ensemble and converted to multimode photonic states by excitation to optically excited levels followed by cooperative spontaneous emission. Among our examples of applications, we demonstrate how two-photon-entangled states can be prepared and implemented in a protocol for a reference-frame-free quantum key distribution and how one-dimensional as well as higher-dimensional cluster states can be produced.

Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value ($\left|K\right|>K_c$), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.

We perform a numerical study of a one-dimensional Fermi-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The $\rho -U/t$ phase diagram is shown for the systems of attractive interactions ($\rho$ is the characteristic density and $U/t$ the interaction strength scaled in units of the hopping parameter). We study the double occupancy, the local central density, and their derivatives. Their roles in detecting the composite phases induced by the trapping potential are discussed in detail.

Gisin’s theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a similar result holds for three-qubit pure entangled states remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy’s nonlocality argument.

We examine the speed and fidelity of several protocols for state or single excitation transfer in finite spin chains subject to diagonal and off-diagonal disorder. We find that, for a given chain length and maximal achievable interspin exchange ($\mathit{XY}$) coupling strength, the optimal static spin-coupling protocol, implementing the fastest state transfer between the two ends of the chain, is more susceptible to off-diagonal ($\mathit{XY}$ coupling) disorder, as compared to a much slower but robust adiabatic transfer protocol with time-dependent coupling strengths.

An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion $Y^{+}$ with an atom $X$. For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations $R$. Since the perturbation parameter is essentially $1/R$, this method is suitable for large $R$. In particular, exchange energies are calculated for ${X_2}^{+}$ systems, where $X$ is H, Li, Na, K, Rb, or Cs.

The laser-induced fluorescence (LIF) $A{\hspace{0.5em}}^1{\Sigma }^{+}–b{\hspace{0.5em}}^3\Pi \to X{\hspace{0.5em}}^1{\Sigma }^{+}$ spectra of the KCs molecule were recorded in a near infrared region by a Fourier-transform spectrometer with a resolution of $0.03$ cm${}^{-1}$. Overall more than 200 collisionally enhanced LIF spectra were rotationally assigned to ${}^{39}\mathrm{K}$${}^{133}\mathrm{Cs}$ and ${}^{41}\mathrm{K}$${}^{133}\mathrm{Cs}$ isotopomers yielding more than 3400 rovibronic term values of the strongly mixed singlet $A{\hspace{0.5em}}^1{\Sigma }^{+}$ and triplet $b{\hspace{0.5em}}^3\Pi$ states with the uncertainty of $0.003–0.01$ cm${}^{-1}$. Experimental data massive starts from the lowest vibrational level $v_A=0$ of the singlet and nonuniformly covers the energy range $E\in [\mathrm{10\; 040},\mathrm{13\; 250}]$ cm${}^{-1}$ with rotational quantum numbers $J^{\prime }\in [7,225]$. Besides the dominating regular $A{\hspace{0.5em}}^1{\Sigma }^{+}–b{\hspace{0.5em}}^3{\Pi }_{\Omega =0}$ interactions, the weak local heterogeneous $A{\hspace{0.5em}}^1{\Sigma }^{+}–b{\hspace{0.5em}}^3{\Pi }_{\Omega =1}$ perturbations have been discovered and analyzed. Coupled-channels deperturbation analysis of the experimental ${}^{39}\mathrm{K}$${}^{133}\mathrm{Cs}$ $e$-parity term values of the $A{\hspace{0.5em}}^1{\Sigma }^{+}–b{\hspace{0.5em}}^3{\Pi }_{\Omega =0,1,2}$ complex was accomplished in the framework of the phenomenological $4\times 4$ Hamiltonian accounting implicitly for regular interactions with the remote ${}^1\Pi$ and ${}^3{\Sigma }^{+}$ states. The diabatic potential energy curves of the $A{\hspace{0.5em}}^1{\Sigma }^{+}$ and $b{\hspace{0.5em}}^3\Pi$ states, as well as relevant spin-orbit coupling matrix elements, were defined analytically with the expanded Morse oscillators model. The obtained parameters reproduce $95\%$ of experimental data field of the ${}^{39}\mathrm{K}$${}^{133}\mathrm{Cs}$ isotopomer with a standard deviation of $0.004$ cm${}^{-1}$, which is consistent with the uncertainty of the experiment. Reliability of the derived parameters was confirmed by a good agreement between the predicted and experimental term values of the ${}^{41}\mathrm{K}$${}^{133}\mathrm{Cs}$ isotopomer. The calculated relative intensity distributions in $A-b\to X$ LIF progressions are also consistent with their experimental counterparts. The deperturbation model was applied for simulation of a pump-dump optical cycle $a{\hspace{0.5em}}^3{\Sigma }^{+}\to A{\hspace{0.5em}}^1{\Sigma }^{+}–b{\hspace{0.5em}}^3\Pi \to X{\hspace{0.5em}}^1{\Sigma }^{+}$ proposed for transformation of ultracold KCs molecules to their absolute ground state $v_X=0;J_X=0$.

Electron attachment to the lanthanide and Hf atoms resulting in the formation of stable excited lanthanide and Hf anions as Regge resonances is explored in the near-threshold electron impact energy region, $E<1.0$ eV. The investigation uses the recent Regge-pole methodology wherein is embedded the electron-electron correlations together with a Thomas-Fermi–type model potential incorporating the crucial core-polarization interaction. The near-threshold electron elastic total cross sections (TCSs) for the lanthanide and Hf atoms are found to be characterized by extremely narrow resonances whose energy positions are identified with the binding energies (BEs) of the resultant anions formed during the collision as Regge resonances. The extracted BEs for excited lanthanide anions are contrasted with those of the most recently calculated electron affinities (ground state BEs). We conclude that the BEs for the ${\mathrm{Pr}}^{-}$, ${\mathrm{Tb}}^{-}$, ${\mathrm{Dy}}^{-}$, ${\mathrm{Ho}}^{-}$, ${\mathrm{Er}}^{-}$, and ${\mathrm{Tm}}^{-}$ anions of O’Malley and Beck [Phys. Rev. A 79, 012511 (2009)] are not identifiable with the electron affinities as claimed. Formation of bound excited anions is identified in the elastic TCSs of all the lanthanide atoms including Hf, except Eu and Gd. The imaginary part of the complex angular momentum $L$, $\mathrm{Im}L$ is used to distinguish between the shape resonances and the bound excited negative ions. These results challenge both experimentalists and theoreticians alike since the excited anions are very weakly bound, but mostly tenuously bound ($\mathrm{BEs}<0.1$ eV). Shape resonances and Ramsauer-Townsend minima are also presented.

Measurements of angular distributions and of the angular dependence of the energy loss of $4-$, $6-$, and $9$-keV protons transmitted through thin Cu and Ag polycrystalline foils are presented. By means of standard multiple-scattering model calculations it is found that a $V(r)\propto r^{-2.8}$ potential leads to significantly better fits of the angular distributions than the standard Thomas Fermi, Lenz-Jensen, or Ziegler-Biersack-Littmark potentials. A theoretical model for the angular dependence of the energy loss based on considering geometric effects on a frictional inelastic energy loss plus an angular-dependent elastic contribution and the effects of foil roughness reproduces the experimental data. This agrees with previous results in Au and Al, therefore extending the applicability of the model to other metallic elements.

We have used the matrix iteration method of Nurhuda and Faisal [Phys. Rev. A 60, 3125 (1999)] to treat ionization of atomic hydrogen by a strong laser pulse. After testing our predictions against a variety of previous calculations, we present ejected-electron spectra as well as angular distributions for few-cycle infrared laser pulses with peak intensities of up to ${10}^{15}$ W/cm${}^2$. It is shown that the convergence of the results with the number of partial waves is a serious issue, which can be managed in a satisfactory way by using the velocity form of the electric dipole operator in connection with an efficient time-propagation scheme.

We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are an important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign, and consequently the interspecies interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above, we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out the fermionic field provides an additional interaction that can decrease or increase bosonic coherence.

We construct a variational wave function to study whether a fully polarized Fermi sea of ultracold atoms is energetically stable against a single spin flip. Our variational wave function contains short-range correlations at least to the same level as Gutzwiller’s projected wave function. For the Hubbard lattice model and the continuum model with pure repulsive interaction, we show that a fully polarized Fermi sea is generally unstable even for infinite repulsive strength. By contrast, for a resonance model, the ferromagnetic state is possible if the $s$-wave scattering length is positive and sufficiently large and the system is prepared to be orthogonal to the molecular bound state. However, we cannot rule out the possibility that more exotic correlations can destabilize the ferromagnetic state.

In this report, we calculate the three tangle of assistance and give the corresponding best possible pure state decomposition of rank-two mixed states for the three-qubit Greenberger-Horne-Zeilinger (GHZ) state and $W$ state. As the three tangle can be transformed into bipartite concurrence with assistance, we achieve a lower bound of the assisted concurrence with local operations and classical communication (LOCC) constraints via these pure state decompositions. It is smaller than the total assisted concurrence, which shows that local assistance alone is not sufficient for maximizing bipartite entanglement. The increase of three tangle is attributed to the genuine multipartite entanglement in the purified state. A genuine four-qubit entanglement measure is calculated for the purified four-qubit state and compared to the three tangle of assistance.

We give results for the orthopositronium decay form factors through one-loop order. We use the form factors to calculate momentum correlations of the final-state photons $\langle k_{Ai}{k}_{Bj}\rangle$ and $\langle {\mathrm{k̂}}_{Ai}{\mathrm{k̂}}_{Bj}\rangle$, including one-loop corrections, for ensembles of initial orthopositronium atoms having arbitrary polarization.

Absolute differential elastic and vibrational excitation cross sections up to $v=11$ were measured for CO in scattering angle ranges extending to ${180}^{°}$ at energies between 0.2 and 5 eV (and an elastic measurement at 10 eV). The lowest angles were $0^{°}$ for inelastic scattering and between $5^{°}$ and ${20}^{°}$ for elastic scattering, depending on energy. Integral cross sections were derived by integrating under the angular distributions and compared with previous beam and swarm measurements. The sum of the integral cross sections agrees very well with the available transmission measurements of the grand total cross section, thus validating the present measurements. The present elastic differential and integral cross sections are in excellent agreement with the best available measurement [Gibson et al., J. Phys. B 29, 3197 (1996)], but the $v=1$ inelastic cross section is about $25\%$ higher. This could have consequences for simulations of cometary and planetary atmospheres.

We use magnetic levitation and a variable-separation dual optical plug to obtain clear spatial interference between two condensates axially separated by up to $0.25$ mm—the largest separation observed with this kind of interferometer. Clear planar fringes are observed using standard (i.e., nontomographic) resonant absorption imaging. The effect of a weak inverted parabola potential on fringe separation is observed and agrees well with theory.